Descent for quasi-coherent sheaves on stacks

TL;DR

This paper provides a homotopy theoretic framework for understanding sheaves on stacks, establishing descent and invariance properties, and offers an alternative proof of a change of rings theorem for quasi-coherent sheaves.

Contribution

It introduces a homotopy theoretic characterization of sheaves on stacks and proves new descent and invariance results, including a novel proof of Hovey's change of rings theorem.

Findings

Homotopy invariance of sheaves on stacks

Generalized descent statements for sheaves and quasi-coherent sheaves

Alternative proof of Hovey's change of rings theorem

Abstract

We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site C. We use this to prove homotopy invariance and generalized descent statements for categories of sheaves and quasi-coherent sheaves. As a corollary we obtain an alternate proof of a generalized change of rings theorem of Hovey.